1. Show that the set of integers S = {a² + b2 : a, b € Z} that can be respresented as the sum of two squares is closed under multiplication. Hint: (a? + b)(e? + d²) = N(a + bi)N(c + di) = N[(a + bi)(c+ di)] = ....

1. Show that the set of integers S = {a² + b2 : a, b € Z} that can be respresented as the sum of two squares is closed under multiplication. Hint: (a? + b)(e? + d²) = N(a + bi)N(c + di) = N[(a + bi)(c+ di)] = ....

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.4: Binary Operations

Problem 9E: 9. The definition of an even integer was stated in Section 1.2. Prove or disprove that the set of...

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Question

1. Show that the set of integers S = {a² + b² : a, b € Z} that can be respresented as
the sum of two squares is closed under multiplication. Hint: (a? + b)(c? + d²) =
N(a + bi)N(c + di) = N[(a + bi)(c + di)] = - ...

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